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We find a conserved monodromy matrix differential operator T in the quantum Self-Dual Yang-Mills (SDYM) system and show that it satisfies the exchange algebra RTT=TTR. From its two infinitesimal forms, we obtain the infinite conserved…
We propose a new quantifier elimination algorithm for the theory of linear real arithmetic. This algorithm uses as subroutine satisfiability modulo this theory, a problem for which there are several implementations available. The quantifier…
In previous works, we devised a differential operator for evaluating typical integrals appearing in the Cachazo-He-Yuan (CHY) forms and in this paper we further streamline this method. We observe that at tree level, the number of free…
Character-based sequence labeling framework is flexible and efficient for Chinese word segmentation (CWS). Recently, many character-based neural models have been applied to CWS. While they obtain good performance, they have two obvious…
Neural machine translation (NMT) heavily relies on word-level modelling to learn semantic representations of input sentences. However, for languages without natural word delimiters (e.g., Chinese) where input sentences have to be tokenized…
By double ideal quotient, we mean $(I:(I:J))$ where ideals $I$ and $J$. In our previous work [11], double ideal quotient and its variants are shown to be very useful for checking prime divisor and generating primary component. Combining…
Contention resolution schemes have proven to be an incredibly powerful concept which allows to tackle a broad class of problems. The framework has been initially designed to handle submodular optimization under various types of constraints,…
In algebraic geometry, there is a reduction algorithm that transforms the unreduced divisor into a unique reduced divisor, which existence is guaranteed by the Riemann-Roch theorem. We discuss application of this algorithm to construction…
The theory of persistence modules on the commutative ladders $CL_n(\tau)$ provides an extension of persistent homology. However, an efficient algorithm to compute the generalized persistence diagrams is still lacking. In this work, we view…
Residuation theory concerns the study of partially ordered algebraic structures, most often monoids, equipped with a weak inverse for the monoidal operator. One of its area of application has been constraint programming, whose key…
We propose a higher-order dimensionality reduction framework based on the Trace Ratio (TR) optimization problem. We establish conditions for existence and uniqueness of solutions and clarify the theoretical connection between the Trace…
We present a space-efficient algorithm to compute the Hilbert class polynomial H_D(X) modulo a positive integer P, based on an explicit form of the Chinese Remainder Theorem. Under the Generalized Riemann Hypothesis, the algorithm uses…
The flourishing blossom of deep learning has witnessed the rapid development of Chinese character recognition. However, it remains a great challenge that the characters for testing may have different distributions from those of the training…
Chinese NER is a difficult undertaking due to the ambiguity of Chinese characters and the absence of word boundaries. Previous work on Chinese NER focus on lexicon-based methods to introduce boundary information and reduce out-of-vocabulary…
Current large language models (LLMs) primarily rely on linear sequence generation and massive parameter counts, yet they severely struggle with complex algorithmic reasoning. While recent reasoning architectures, such as the Hierarchical…
Encoding the electronic structure of molecules using 2-electron reduced density matrices (2RDMs) as opposed to many-body wave functions has been a decades-long quest as the 2RDM contains sufficient information to compute the exact molecular…
Several quantum algorithms for linear algebra problems, and in particular quantum machine learning problems, have been "dequantized" in the past few years. These dequantization results typically hold when classical algorithms can access the…
We develop a polynomial reduction procedure that transforms any gauge fixed CHY amplitude integrand for $n$ scattering particles into a $\sigma$-moduli multivariate polynomial of what we call the $\textit{standard form}$. We show that a…
Iterative majorize-minimize (MM) (also called optimization transfer) algorithms solve challenging numerical optimization problems by solving a series of "easier" optimization problems that are constructed to guarantee monotonic descent of…
Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to…